Fiber optics are an important part of our modern internet. In these fibers, two different glasses are used to confine the light by total internal reflection at the critical angle for the interface between the core (n_core = 1.514 ) and the cladding (n_cladding = 1.43). Required:
a. Numerically, what is the largest angle (in degrees) a ray will make with respect to the interface of the fiber θ_max, and still experience total internal reflection?
b. Suppose you wanted the largest angle at which total internal reflection occurred to be θ_max = 5 degrees. What index of refraction does the cladding need if the core is unchanged?

In the future, people will only enjoy one sport: electrodisc. in this sport, you gain points when you cause metallic discs hovering on a field to exchange charge. you are an electrodisc player playing the popular four disc variant. the disks have charges of qa = −8.0 µc, qb = −2.0 µc, qc = +5.0 µc, and qd = +12.0 µc. (1) you bring two disks together and then separate them. you measure the resulting charge of these two disks and find that it is +5.0 µc per disk. which two disks did you bring together? (a) a and b (b) a and c (c)a and d (d)b and c(e) b and d (f) c and d. (2) you bring three disks together and then separate them. you measure the resulting charge of these three disks and find that it is +3.0 µc per disk. which three disks did you bring together? a, b, and c (a) a, b, and d (c) a, c, and d (d) b, c, and d. (3) given the resulting charge of each disk measured in (b) is +3.0 µc, how many electrons would you need to add to a disk of this charge to electrically neutralize it? electrons